Junior maths challenge 2025

I believe it was inevitable that UKMT had to add more difficult / trickier problems to push the scores down, as it was mentioned in the thread above. Still will be some who scored maximum, but fewer than usual

I think it would be trickier if 10 and 20 were also included as answer options 🙂

Am I the only person that thought question 17 was unfair?
If you know you are writing down a six digit number you could in theory imagine 6 boxes , you may write down a 1 in the first box , you then write down the other two 1s in two of the other boxes. This gives 20 possibilities.
You then realise this is not one of the possible answers, you panic, waste time etc.
Maths generally punishes those who make unsubstantiated assumptions but here those that assumed the digits were written down in order ( not given) were rewarded.

It's interesting that you comment on this question, it's one of the only ones that threw my DS who has never had any special teaching or prep for the maths challenge they just get told the day before that they are doing it.
Looking at the published solutions he thinks he's scored 123 so will probably just miss out on the Olympiad.

Does anyone know when the results are due to come out? I’m not hugely hopeful for DS because he looked at the answers and was annoyed about how many he’d gotten wrong. But being in Y5, and without any proper prep, I’d be chuffed if he got anything at all. Let’s see. Would be nice for his self confidence.

He has always made up his own maths problems for fun, and has loved numbers ever since he was a baby. Sadly he’s been born into the world’s least mathematical family (I have two degrees in English Literature, but barely know my times tables!) Poor child.

DD took it for the last time this year and knew she would qualify for JMO so one more go at it. She was taught by me on and off but she is more into sports than doing maths nowadays. Having said that, she is keen to do well in her last JMO. Next year it will be the last Cayley etc.

There are classes for Olympiad training here but I found them difficult to join. All kids are at different ability level so doing 1 to 1 training would be best.

1. y8 parallel tutorial programme did teach that exact method of treating a grouped unit of k as one unit so you now are arranging n-k units but then being careful to correctly work out both
   firstly the original number of possible ways of choosing that k from within the larger group and secondly any possible sub-arrangements within that group of k (if it matters and in this question it does not).
   Method becomes good precisely in case when the k sub arrangements are significant.
   Sincerely doubt even strong math kids would arrive at that approach without having seen it

2. but always good to use symmetry/limit/alteration to the question to check combinatorics answers make actual sense

3. I think my point still remains that this is "casework" within a combinatorics question which I've not seen before at JMC level

4. someone else mentioned this, but I too found some of the wording of questions quite unclear; bound to catch my DS out!

The case with ties splits into three sub-cases: 1st & 2nd are tied, 2nd & 3rd are tied, 3rd & 4th are tied. These sub-cases are equivalent in that there are two individual positions and one tied place, so we have to work out only one sub-case and can multiply by 3. There are four ways to choose one of the individual positions, three ways to choose the other individual position and... only one way to choose the remaining two people in the tie. So 4x3x1 = 12 for each sub-case, 3x12 = 36 for the case with ties. @user149799568

My method is the same as yours. However, my DD just now solved it using the exact tactical method found in the official solution. She spontaneously treated the two tied individuals as one unit to simplify the arrangement—a technique she likely picked up from a US maths competition book. I prefer the approach we used because it is theory-free and less prone to error.

Interesting comments here that this year's challenge was harder. DS noticed no real difference. But then last year he felt the Kangaroo was easier than the main jmc and got a considerably higher K mark than jmc!

I agree, I had the answers to both Question 7 and Question 11 pretty much at the time I finished reading them.

Per my previous post:

However, it is true that contestants will be strong or weak in different areas, e.g., combinatorics, geometry, number theory, and algebra, so I will accept that my statement is probably too general.

That said, the differences will be less pronounced over an entire paper than for individual questions.

@Statistico Questions 24 and 25 are typically the most interesting ones on these papers. It's true that there hasn't been a combinatorics problem in those spots for several years, but that doesn't mean that this one was particularly difficult. I don't like their solution and think the problem is simpler than it implies.

First you need to recognize there are two cases: no ties and with one tie. Once you do that, it's obvious that there can be no overlap.

The case with no ties is straightforward enough: four ways for one position, three ways for another position, two ways for another position and one way for the remaining position. The product rule 4x3x2x1 = 24.

The case with ties splits into three sub-cases: 1st & 2nd are tied, 2nd & 3rd are tied, 3rd & 4th are tied. These sub-cases are equivalent in that there are two individual positions and one tied place, so we have to work out only one sub-case and can multiply by 3. There are four ways to choose one of the individual positions, three ways to choose the other individual position and... only one way to choose the remaining two people in the tie. So 4x3x1 = 12 for each sub-case, 3x12 = 36 for the case with ties.

However, it is true that contestants will be strong or weak in different areas, e.g., combinatorics, geometry, number theory, and algebra, so I will accept that my statement is probably too general.

As an aside, I think this year's Question 24 is rather easy for its slot. The only saving grace is that many children will have either forgotten to, or run out of time to, check the feasibility of N = 5 as a solution.

@user149799568 Thanks for that, and the explanation too putting it in context.

if I'm not mistaken I think you were the person who's DC fell foul of the dodgy question last yr, hope it all goes well this time around.

I'm starting to wonder about my DD. Before hearing her mark I'd like to see a low threshold, wouldnt we all, say 102 would be nice (125)+(76). While I agree with your 105 I'll stick by a prediction of a few days ago where I said I think 90s is more likely than 110s for Olympiad qual. Like with the IMC I believe the raised difficulty will have caught out many candidates, causing them to underperform.

It's a strange one for us, JMO qual yr7 was great, IMO yr8 even better, and now she could miss out on what relatively is the easiest of the 3. I do think there's maybe a 25% chance of this happening. That said for 2026 if someone said my DD could be one of IMO or JMO there would be only one choice, so I'm relaxed about the situation.

@Jonny234 my approach of measuring how long it takes to do a paper is most useful when someone is fully time limited. Specifically, that means that they were still making progress when time ran out and could have made more progress if they had another 5 minutes. If, however, a child ran out of accessible questions after 30 minutes on last year's paper, the additional "length" wouldn't affect them in the same way. That said, as the additional length is due to there being fewer easy questions, that same child would probably fewer accessible questions on this year's paper, but I don't have a good guess of how many fewer.

The only information I can give you about the 2026 JMC compared with recent IMCs is that they took me similar amounts of time to finish. However, I wouldn't draw the conclusion that a child with less knowledge and experience would find them of the same "difficulty".

I was able to complete the 2026 JMC in 45 minutes @user149799568

It’s very interesting. There are some questions I can solve in seconds, while DD spends quite a long time on them.

Take Q7 for example. I know parity, so I instantly get the answer in about five seconds, while DD gets stuck for a long time. As for Q9, I just tried the candidate answers and used multiples to work it out. I got the answer well under a minute. DD spent almost 10 minutes on it. She first tried working it out in her head, then listed and drew all possibilities one by one.

Many questions are like this. Some have confusing wording, which is also hard for DD to understand.

While comparison to the IMC is interesting I have to disagree that "none of the individual questions this year were unusually difficult or inaccessible".
Just one example:
Q25 on this year's JMC is combinatorics with case work I.e. two cases must be fully explored using product rule within each (pairs exception in one) and then combined (also complementary counting not useful) to obtain answer.

Admittedly the final question on the paper but I'm not sure I've seen that asked on a JMC before. Happy to be corrected.

IMHO definitely some harder questions, not just questions taking longer.
My DS managed 24, ran out of time on Q25 which is a shame as exact kind of 'combinatorics casework' problem y8 parallel academy tutorials were covering at end of autumn term.
Having now seen actual paper I would forget my earlier throwaway prediction that JMO boundary might still be 115. This was largely based on DS's reporting of 24 solid answers. However knowing him well, and looking at problems I suspect several of his answers won't quite be correct.
105 seems an excellent estimate for JMO boundary

Many thanks for the depth and level of detail @user149799568 I knew you'd be on the ball with this which is why I specifically asked.

I'm a bit of a rush atm so won't go too deep.

Like I said in one of the earlier posts some who sat both 2026 SMC and IMC claimed the latter was harder due to time pressure but for somebody as capable as yourself it seemed around equal.

I will have a good look through that document in due course, its a very handy guide.

A minor one, being pedantic, I think perhaps from my anecdotal evidence from my DD that your 4-5 ranges at the end are more like 2-4 for her. For example, she was answering with some degree of confidence say 23 in her IMC mocks and ended up answering 21 in the exam. Last year in tthe JMC she was very confident on 23 and this year it's 20. But generally the point is the same.

With regards to the question I already know that the 2026 IMC was harder than the 2026 JMC. The question i asked was.....

"The JMC this year seems closer to say 2023-2025 IMC's rather than previous years JMC's and this years IMC. If @user149799568 has the time available I'd appreciate if they could look at one of the 2023-2025 IMC papers and see how they think it compares to this years JMC."

Reading between the lines of what you say it would be interesting to hear your thoughts. From my side I just know my DD was scoring say 105-118 with a 123 thrown in on IMC mocks, and now she's taken the 2026 JMC I envisage perhaps a similar score indicating to me these are perhaps of similaar difficulty.

@Jonny234 The question "which paper is more difficult" is imprecise, so I'm going to give an imprecise answer.

For me, the 2025 SMC and 2026 IMC were similar in "length" and the 2026 JMC was shorter. What I means is that I was able to complete the 2025 SMC in just under 90 minutes and the 2026 IMC in just under 60 minutes, whereas I was able to complete the 2026 JMC in 45 minutes. Obviously, the 2025 SMC took me longer than the 2026 IMC, so was "harder" in one sense but, given the time limits (90 minutes for the SMC vs 60 minutes for the IMC), I was under the same amount of time pressure on both, and under less time pressure on the 2026 JMC.

The level of the syllabus covered in an exam provides a different measure of difficulty. A normal Year 8 student would find the IMC less accessible than the JMC in the sense that they would be less familiar with some of the topics queried. I don't think anything like Question 21 on the 2026 IMC (involving cubic polynomials) has been asked on the JMC, at least not recently. In general, the IMC assumes greater familiarity with exponents and more advanced algebra than the JMC, e.g., quadratic equations. Similarly, the SMC typically asks about more advanced functions, sequences and polynomials than the IMC, albeit rarely anything not introduced in the GCSE Math syllabus. This document provides some information about differences between the topics addressed in different UKMT Challenges as well as the Olympiads.

To answer your specific questions:

I regard the 2026 JMC as easier than the 2026 IMC both in terms of the level of math required and in terms of being less time pressured (for the target demographic) as well as in the absolute sense that I believe that nearly all students who take both papers would get a higher score on the 2026 JMC than on the 2026 IMC.

Comparing this year's papers with other recent papers, I think the 2025 SMC was pretty similar to the previous several years' papers. I believe the 2026 IMC was 4-5 questions longer than the previous several years' papers in the sense that most students would have solved 4-5 fewer questions within the time limit, but none of the individual questions this year were unusually difficult or inaccessible. I feel the same way about the 2026 JMC; 4-5 questions longer, but all questions being within the range of those on the previous several years' papers.

I asked my DD about time pressure and she said she had enough time. That said I had specifically highlighted to her pre exam even on the morning of the exam to be careful about dawdling in the early stages and then playing catchup. Seems like she listened, something which is becoming increasingly difficult as she gets older :)

Then something else that she's able to do recently, in the last year or so is knowing she doesnt have to take questions in order. if she sees one too difficult or time consuming she skips and revisits later. This comes with age.

There's these and other little things that come with age, maturity, and exposure.

Finally with respect to time pressure when my DD took the Cayley, Q1&2 are normally seen as the easier questions. She told me Q1 alone took her 50 mins but was a full solution with full marks.

It was certainly a “challenge” this year. However, for it to be a meaningful challenge, any student at a Gold level or above (the top 10%) should ideally have enough time to at least address every question. What is the point of a beautiful, challenging problem if most students never have the time to think it through?
Sixty minutes for 25 questions is quite short, especially compared to the two hours allowed for only six problems in the JMO. Of course, in the JMO you have to show your full working, but even in the JMC, you still need time to work the solutions out. On the other hand, including too many easy, school-level questions defeats the purpose of the competition.
That is why I believe a 20-question format—consisting of 5 easy and 15 hard questions—would be ideal. This would give most students some initial confidence while differentiating the top performers based on their ability to solve hard problems, rather than their ability to beat the clock.

The difficulty increasing is a good thing. Many on here last yr who had very able kids fell foul of one question having slightly ambiguous wording and fell below a threshold. I'd be annoyed if that happened to my DD.

This year is a lot better, however as I suspected all along (and discussed with my DD) it was more difficult than previous years and this will have come as a surprise for many candidates.

Now that the paper and solutions are out, we can discuss more freely.
@user149799568

Somehow I missed your post.

This paper takes substantially longer to complete than most of the other recent ones. Children at the top end who were already time pressured will probably have addressed 4-5 fewer questions than in the last two papers.

Yes. My DD left 6 unanswered.

The first couple of "gimme" problems were no more difficult but were more tedious (took longer to do) than in recent papers.

And that is very time-consuming, which will affect their ability to handle the subsequent problems.

Question 6 felt out of place. Problems involving combinatorics (listing all possibilities) rarely appeared before Question 16 in past papers.
Similarly with Question 7. Problems involving number theory (primes, parity), were rarely before Question 16 and usually after Question 21. Same with Question 11, although I thought Question 11 would have been easier than Question 7 for most children.
Parity appears twice, in Q7 and Q11, while calculating the overlap appears three times: in Q14, Q23, and Q24. It isn't ideal for the same theme to appear more than once in a single paper.

That said, none of the individual problems were more difficult than any that had appeared in other recent papers.It's just that there were more of the more difficult ones than in other recent papers, e.g., Question 21 could have been a Question 24 or 25.
I agree. I believe my DD could solve most of them if given a reasonable amount of time. It is the way the paper is organized that lowers actual performance. It is supposed to be 15 easy questions followed by 10 hard ones, but now, 10 of those "easy" questions have become hard ones. Next time I would recommend reducing the total number of questions to 20—perhaps 5 easy and 15 hard ones.

My guess is that the Gold boundary will be around 75, Kangaroo around 85, and the JMO qualifying score will be around 105.
My estimate is probably 10 points less than your estimate.

I agree with your theory. For example, some students in her class finished very early and left to play, so of course, they wouldn't appreciate the difficulty, though they definitely won't get a medal either. In fact, unless someone has prepared and has high expectations for themselves, they probably wouldn't even notice the difference in difficulty from past papers.

Actually I really like the general difficulty level of the JMC this year and believe it is good for stretching able students. However, I dislike the difficulty relative to the time constraints, as well as the way questions are organized and the unnecessary attempts to confuse participants. Take Question 20, for example: "In Kush’s Cake Shop, there are chocolate cakes, cherry cakes, cream cakes, and coffee cakes..." The problem itself is not that difficult, but it seems to create needless confusion by using highly similar and easily mistaken names. This also happens in the earlier, easier questions. Is it harder than the IMC? Of course not. But it is certainly more frustrating—even just looking at it gives me a headache.

You were quoting me and not @Statistico

FYI. I looked into the IMC a lot post exam before the results arrived and you had 2 conflicting stories/ accounts. The first was a lot of people saying it was about the same as last year, and then a few saying it was brutal and nothing like they'd experienced before. On balance you'd think the majority was correct.

In actual fact both were correct. The gap was all in the nuance.

The majority (gold and below) who might answer the first 15 and then have a stab at a pick of the last few saw no discernable difference to past papers.

It was only the top performers, perhaps expecting to answer 23 or so actually felt how bad the last 8 or so were.

If I had to conclude anything it's that there is a chance some questions 6-15 of the JMC could have been more difficult than the same number ones in the IMC. @Jonny234
That was my point: because of 6-15 hard questions, the resulting time-consuming and stress leaves students without enough time to properly address simpler problems, such as q23, which then appear difficult from a performance standpoint. I also agree that, given sufficient time for both, a student's IMC score would be lower than their JMC score.
For a student who has been through JMO and can easily handle the IMC, time pressure isn't a major issue. However, for my DD, who is younger and currently performing between the Kangaroo and JMO levels, the time constraint is a real challenge.

@swdd What I'm seeing and hearing I don't believe that is the case.

The IMC this yr was universally brutal by the accounts of the top candidates but like i say in a different way to the JMC. The IMC seemed as normal till about Q16 and then ramped up horribly, in the JMC it seemed to be from Q6 but less markedly but of course more difficult. If I had to conclude anything it's that there is a chance some questions 6-15 of the JMC could have been more difficult than the same number ones in the IMC.

That said I just go off what I hear from my DD and read, I do know from this time last year @user149799568 is very good and on top of gauging the difficulty of the questions. I'll stick by what I alluded to earlier. The JMC this year seems closer to say 2023-2025 IMC's rather than previous years JMC's and this years IMC. If @user149799568 has the time available I'd appreciate if they could look at one of the 2023-2025 IMC papers and see how they think it compares to this years JMC.